It is a balance. Atoms want naturally to have a number of electrons at certain levels called shells. The zero level is zero electrons, the first level is two electrons, and the second level is 8 electrons. Oxygen has 8 electrons, 2 for the first shell and only 6 for the second. To be stable, oxygen really wants two more electrons to be stable. Hydrogen has only 1 electron. In the case of H2O, the hydrogens give up their own electron to fill in the oxygen’s second shell, creating a molecule with 3 atoms at stable electron shells, 2 hydrogens at level 0 and 1 oxygen at level 2. In the case of H2O2, each hydrogen loans its electron to an oxygen but neither of the oxygen has enough electrons to be stable, each has 9 but wants 10. The closer an atom is to getting its desired number of electrons the more it wants to rip neighboring molecules apart so it can reach that stability. With H2O2, it is even more enhanced by the fact that there are 2 oxygens that desperately want just one more electron.
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